let x be an n-square complex matrix with the cartesian decomposition x = a + i b, where a and b are n times n hermitian matrices. it is known that $vert x vert_p^2 leq 2(vert a vert_p^2 + vert b vert_p^2)$, where $p geq 2$ and $vert . vert_p$ is the schatten p-norm. in this paper, this inequality and some of its improvements ...
